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Abstract
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of 4+1 dimensional disordered system. We use the holographic viewpoint to provide the conjectural explanation of these properties. The delocalization of all modes in the confined phase is related to the θ=π - like phenomena when the fermions are delocalized on domain walls. It is conjectured that the localized modes separated by mobility edge from the rest of the spectrum in deconfined QCD correspond to the near-horizon region in the holographic dual.
Highlights
The 4D Euclidean Dirac operator iγμDμ spectrum in QCD is the important observable both in the confined and deconfined phases
It is conjectured that the localized modes separated by mobility edge from the rest of the spectrum in deconfined QCD correspond to the near-horizon region in the holographic dual
The lattice studies demonstrate [11, 13] that all eigenmodes of 4d Euclidean Dirac operator in the confined phase are delocalized, and it behaves as 4d metal
Summary
The 4D Euclidean Dirac operator iγμDμ spectrum in QCD is the important observable both in the confined and deconfined phases. We assume that the delocalization of all modes in the confined phase is related to the existence of the domain walls at θ = π The relevance of this regime follows from the fact that the eigenfunction of the Dirac operator corresponds to the quark with imaginary mass and the phase of the mass is traded by the axial anomaly to the non-vanishing θ-term. It is natural to question how the emergence of BH in the deconfined phase and the mobility edge in the Euclidean 4D Dirac operator spectrum are correlated.
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